已知方程x^2+y^2-2(m+3)x+2(1-4m^2)y+16m^4+9=0表示一个圆.1 求实数m的取值范围 2

X^2+Y^2-2(m+3)X+2(1-4m^2)Y+16m^4+9=0
(X-(m+3))^2+(Y+1-4m^2)^2=(m+3)^2+(1-4m^2)^2-9-16m^4
等式左边可以化为
左=(m+3)^2+(1-4m^2)^2-9-16m^4
=m^2+6m+9+1-8m^2+16m^4-9-16m^4
=-7m^2+6m+1
1.
左=-(7m+1)(m-1)>0
=> -1/7